Question: Simplify the following expression: $\sqrt{160}+\sqrt{10}-\sqrt{40}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{160}+\sqrt{10}-\sqrt{40}$ $= \sqrt{16 \cdot 10}+\sqrt{10}-\sqrt{4 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{10}+\sqrt{10}-\sqrt{4} \cdot \sqrt{10}$ $= 4\sqrt{10}+\sqrt{10}-2\sqrt{10}$ Finally, simplify by combining the terms. $= ( 4 + 1 - 2 )\sqrt{10} = 3\sqrt{10}$